1. Field of the Invention
The present invention relates to a method of localizing a robot. More particularly, the present invention relates to a method of localizing a mobile robot by using a Kalman filter with constrains as well as to a robot adapted to localize itself using this method.
2. Description of the Related Art
Various types of robots have recently appeared as a result of technological advancement. Particularly, there are robots capable of moving inside a house by themselves in order to do household labor. Self-localization of mobile robots is very important, and many methods have been proposed to accomplish this feature. In order to localize a robot, it is customary to attach an encoder (or odometer) to a driving unit (e.g., a wheel) of the robot or mount a gyroscope onto the robot in order to measure the correct rotational angle of the robot. However, slippage or mechanical drift of a wheel, when a robot is localized, causes error. Although such error may be negligible at first, it may accumulate and cause significant problems.
A Kalman filter algorithm is conventionally used to localize a robot. However, due to the absence of constraints, estimated parameters often violate physical constraints. For example, when the wheel base distance of a mobile robot is Wb and the physical range of Wb is 0.3 m≦Wb≦0.4 m, the estimated Wb may be outside this range. In the case of SLAM (simultaneous localization and mapping), which uses ceiling vision based on the Kalman filter, the estimated ceiling height z must be in a certain range, e.g., 2.4 m≦Wb≦2.5 m. However, the estimated z may be outside this range.
A conventional Indirect Kalman filtering method, proposed by Chung et al., uses a combination of an odometry error model (or encoder error model) and a gyroscope angular error model as a process model, and uses the measured angle difference between a gyroscope and an odometer as the measurement model. The indirect Kalman filter is described in detail in “Accurate Mobile Robot Dead-reckoning With a Precision-calibrated Fiber-optic Gyroscope,” by H. Chung, L. Ojeda, and J. Borenstein in IEEE Transactions on Robotics and Automation, vol. 17, Issue 1, pp.80-84, February 2001. The state equation of the conventional indirect Kalman filter method includes various parameter estimates, such as error in robot pose estimated by the encoder, error in robot angle estimated by the gyroscope, scale factor of the odometry, and wheel tread distance, as well as the state of various sources of noise, as shown in FIG. 3.
In FIG. 3, state variables labeled 310 refer to error in robot pose estimated by the encoder; state variables labeled 320 refer to error in robot heading angle estimated by the gyroscope; state variables labeled 330 refer to various parameter estimations; and a state variable labeled 340 refers to noise.
In FIG. 3, SR(k) and SL(k) refer to the scale factor errors of the right and left encoders, respectively, and D(k) refers to the tread error, i.e., the error introduced by variations in the distance between the left and right wheels.
However, an indirect Kalman filter based on the state equation shown in FIG. 3 has poor observability. Particularly, although the state vector in the state equation of FIG. 3 has a dimension of 9, the rank of the observability matrix is merely 2 under an assumption that the state transition matrix is in a steady state of a time-invariant system.
The fact that the state of the robot is not fully observable makes it impossible to guarantee whether or not remaining states converge. More particularly, since nothing but a rotational angle state is included in the observation matrix, it cannot be confirmed whether or not a state, such as error in position (x, y) of the robot, converges to a true value. Even when the system is in a time-varying condition, the observability matrix has a rank of 6 and is still unstable.
Therefore, in order to solve this problem, the present invention introduces an additional observable system state for estimation.
Therefore, it is also necessary to both reduce error in localizing a robot so that the stability of the robot is guaranteed, and make parameters estimated when applying a Kalman filter satisfy physical constraints so that the performance of the robot is improved.
A measurement equation according to the related art is defined by equation (6) below and shown in FIG. 6. It is clear from FIG. 6 that only an angular state is included in the observation matrix H.Measurement equation=orientation of robot estimated by encoder−orientation of robot estimated by gyroscope+noise   (6)In FIG. 6, “v” refers to measurement noise.